(1) Field of the Invention
This invention relates to a composite material with negative permeability.
(2) Description of the Art
Conventional materials exhibit positive magnetic permeability p and positive dielectric permittivity ε for electromagnetic radiation at microwave frequencies, which corresponds to the radiation in such a material having an electric field E, magnetic field H and wave vector k collectively forming a right-handed triplet of vectors; such materials also exhibit positive refractive index (PRI). Microwave frequencies are those at and above 1 GHz.
Permittivity εand permeability μ are both complex numbers, so they have real (ε′, μ′) and imaginary (ε″, μ″) components. They are given by:μ=μ′−i.μ″, and   (1)ε=ε′−i.ε″.   (2)
A material has a negative refractive index at a particular frequency of electromagnetic radiation if its permittivity and permeability are both simultaneously negative at that frequency: negative refractive index corresponds to the phase velocity (i.e. wave vector k) being reversed and the radiation's E, H and k vectors forming a left-handed triplet of vectors. Negative permittivity and negative permeability are defined as the real components (ε′, μ′) of these parameters possessing negative values. In negative refractive index materials, radiation refracts in the opposite direction to conventional PRI materials. Such materials are also known as left-handed materials and have been shown to have a number of potentially advantageous properties. Materials with negative permittivity and/or permeability and negative refractive index have a number of applications: e.g. radomes to protect antennas, signal filtering, radiation dissipation at anechoic chamber walls, and radiation shields to comply with regulations laid down by regulatory bodies and prevent electromagnetic interference.
Smith D. R., Pendry J. B., Wiltshire M. C. K., “Metamaterials and Negative Refractive index”, Science, 305, 1788, 2004 disclose artificial media (also known as ‘Metamaterials’) with negative permittivity or permeability, e.g. periodically spaced wires for negative permittivity and split ring resonators for negative permeability.
Composite materials which have negative permittivity or negative permeability are known. A thesis, “Electrical Percolation and the Design of Functional Electromagnetic Materials” by Ian J. Youngs, University of London, England, December 2001, has a discussion of the background to and physics of such materials. Published International Application No. WO 2005/052953 A1 discloses negative permittivity composite materials which consist of electrically conducting particles in an insulating matrix, e.g. nanospheres of silver 15 nm or 100 nm in diameter randomly dispersed in paraffin wax or polytetrafluoroethylene (PTFE) spheres 1 μm or 100 μm in diameter.
U.S. Pat. No. 5,498,644 to N J Reo discloses a composite material for electromagnetic interference shielding, the material comprising electrically conducting, magnetic, silver coated micro-balloons incorporated in a silicone elastomer: there is no disclosure of negative permeability. GB 1224735 to G I Andrews et al. discloses a composite material for self lubricating bearings and comprising metal particles such as iron, steel or cobalt incorporated in a polymer such as PTFE: here again there is no disclosure of negative permeability.
EP 0951023 discloses a magnetic composite comprising flaky magnetic powder in an organic binder. All examples of the composite exhibited positive magnetic permeability of approximately 4 or greater at frequencies up to 1000 MHz (see FIG. 2).
U.S. Pat. No. 6,054,210 relates to a magnetic article comprising oblate spheroidal ferromagnetic particles embedded in a polymer binder. There is no disclosure of negative magnetic permeability.
EP 1661647 discloses a magnetic composite sheet comprising a soft flaky magnetic powder dispersed in chlorinated polyethylene. Negative magnetic permeability is not disclosed.
U.S. Pat. No. 5,925,455 discloses a composite comprising alternating layers of dielectric flakes and magnetic flakes dispersed in a polymer binder. There is no disclosure of negative magnetic permeability.
GB 1299035 discloses a composite comprising a polymer encapsulated combination of magnetic particles and a solid or paste or dye or pigment. From disclosed weight fractions, the magnetic particles are less than 5% by volume of the capsules, and even less of the capsule/polymer dispersion as a whole: this is unsuitable for negative magnetic permeability.
WO 2006/078658 A1 discloses a device incorporating multiple helices and exhibiting negative magnetic permeability: it is similar to conventional artificially engineered negative permeability media. There is no disclosure of a composite material incorporating magnetic particles dispersed in another medium.
Metals contain significant numbers of electronic charges that are free to move through the bulk of the material (the conduction band electrons). An electric field applied to a metal therefore induces a macroscopic electrical transport current in the material.
The frequency response of the permittivity of metals is determined by weakly bound (effectively free) electrons in the conduction band. At low frequencies, the electrons oscillate in phase with an applied electric field. However, at a certain characteristic frequency, oscillation in phase with the applied field can no longer be supported, and resonance occurs. Free electrons in a metal can be considered to be a plasma, i.e. a gas consisting partly or wholly of charged particles. The electron gas may be two dimensional and held between two electrodes. Under an applied electric field the electrons will move in the opposite direction to the field resulting in charges of opposite sign at either end of the plasma. It can be shown that the electrons oscillate at a characteristic frequency ωp referred to as the plasma frequency given byωp2=(e2lmeε0)N   (3)
where e and me are the electronic charge and mass. ε0 is the permittivity of free space and N is the number of electrons in the plasma.
For metals, εp is in the ultraviolet. For frequencies above εp, metals can be considered to act like dielectrics, i.e. they have a positive permittivity and support a propagating electromagnetic wave.
The oscillation of a plasma may be quantised: a plasmon is the unit of quantisation. The action of plasmons produces a complex dielectric function (or permittivity) ε(ω) of the form:
                              ɛ          ⁡                      (            ω            )                          =                  1          -                                    ω              p              2                                      ω              ⁡                              (                                  ω                  +                  ⅈγ                                )                                                                        (        4        )            
For frequencies below ωp, metals exhibit a negative permittivity, and electromagnetic radiation cannot propagate but instead decays exponentially.
Unlike metals, dielectrics contain only bound electrons, and become polarised under an applied electric field E. A time varying electric field E(t) of frequency ω exerts a force on an electron giving rise to an equation of motion for the electron of:
                                                        m              e                        ⁢                                                            ⅆ                  2                                ⁢                x                                            ⅆ                                  t                  2                                                              +                                    m              e                        ⁢            γ            ⁢                                          ⅆ                x                                            ⅆ                t                                              +                                    m              e                        ⁢                          ω              0              2                        ⁢            x                    -                      e            ⁢                                                  ⁢                          E              0                        ⁢            cos            ⁢                                                  ⁢            ω            ⁢                                                  ⁢            t                          =        0                            (        5        )            where e and me are the electronic charge and mass, E0 is the electric field magnitude, ω0 is a characteristic (or resonant) frequency, and x is a distance moved by an electron under the electric field; meydx/dt is a damping term representing the time delay between applying the electric field and establishing polarisation equilibrium. The resulting dielectric polarisation due to N electrons is given by P=exN, which is related to the dielectric permittivity ε byε=ε0+P(t)lE(t)   (6)
Hence the permittivity of the dielectric is given by
                    ɛ        =                              ɛ            0                    +                                                                      e                  2                                ⁢                N                                            m                e                                      ⁢                          1                              (                                                      ω                    0                    2                                    -                                      ω                    2                                    -                  ⅈγω                                )                                                                        (        7        )            
The characteristic frequency ω0 is indicated by a maximum in the imaginary permittivity and represents radiation absorption from electron-phonon interactions. Over a frequency range containing an absorption band, the real permittivity is frequency dependent
Identifying materials with different permittivities can enable the design of components and devices with different electromagnetic functionality (for example, different levels of reflection, transmission and absorption) operating over specific regions of the electromagnetic spectrum. However, the range of naturally occurring permittivities is not adequate for many purposes, which has led to development of composite media with complex permittivity that can be tailored to suit a particular use.
It has been known for some time [Bracewell R. Wireless Engineer, p. 320, 1954] that periodic arrays of metal elements can be used to form composite media (metamaterials) with plasma frequencies lower than that of a conventional bulk metal. More recently, in Phys. Rev. Letters, vol. 76, p. 4773, 1996, Pendry J et al. demonstrated that a periodic lattice of thin metallic wires could exhibit a plasma frequency in the microwave region given by;ωp≈2πc2/(d2 ln(d/r))   (10)
Periodic arrangements of metallic elements, such as split ring resonators, are known to exhibit negative magnetic permeability at microwave frequencies: see Pendry J et al., IEEE Transactions on Microwave Theory and Techniques, vol. 47, p 2075, 1999. Such arrangements are however difficult and costly to fabricate. Holloway et al, IEEE Transactions on Antennas and Propagation, Vol 51, No. 10, October 2003 have speculated that it may be possible to produce a material with both negative permeability and negative permittivity in a composite material consisting of insulating magneto-dielectric spherical particles embedded in an insulating matrix.
It is desirable to find negative permeability materials in which the magnetic component of the electromagnetic wave will die away exponentially. A composite material with a tailored plasma frequency would also be valuable. The scientific literature has reported that a plasma frequency has been achieved at microwave or radio frequency.
The magnetic properties of materials result from electron motion, which leads to magnetic dipoles within magnetic materials. Under equilibrium conditions, magnetocrystalline anisotropy (an intrinsic property of a material) causes a particle to have a magnetic moment which lies parallel to the particle's magnetic axis (which defines preferred crystalline axes for magnetisation, as dictated by the preferred direction of magnetic dipoles). When a field is applied, the magnetic moment deviates from the magnetic axis and is subjected to a mechanical torque, which causes precession (also known as Larmor precession) about the axis. In ‘real’ systems, where damping resulting from imperfections is also present, the magnetic moment has a motion described by the following Landau and Lifshitz equation [Landau L. D., Lifshitz E. M., Pitaevskii L. P., “Electrodynamics of Continuous Media”, (Butterworth-Heinenann, Oxford, 1998)]:
                                          ⅆ                          m              ⁡                              (                t                )                                                          ⅆ            t                          =                              -                          μ              0                                ⁢                                    γ              m                        (                                          Γ                ⁡                                  (                  t                  )                                            +                                                λ                                      m                    2                                                  ⁡                                  [                                                            m                      ⁡                                              (                        t                        )                                                              ×                                          Γ                      ⁡                                              (                        t                        )                                                                              ]                                                      )                                              (        11        )            
where μ0 is the free space permeability, γm is the gyromagnetic ratio, λ is a damping constant and Γ(t) is total torque exerted on the magnetic dipole moment, m, by both magnetic anisotropy and external magnetic field.
The rate at which a magnetic moment precesses about an axis is given by the Larmor or Ferromagnetic Resonance Frequency, fL. Permeability spectra exhibit a resonance at this frequency, because energy is absorbed from an incident field in order to overcome damping of the precessional motion: fL is given by:
                              f          L                =                                            μ              0                        ⁢                          γ              m                        ⁢                          H              A                                            2            ⁢            π                                              (        12        )            where HA represents an anisotropy field associated with the direction of the magnetic moment, m, with respect to crystallographic axes.